Problem $4$

A cantilever spring $($Fig$.3-44)$ is subject to fluctuating loading with $F_{\text{m}\text{a}\text{x}}=222N$ and $F_{\text{m}\text{i}\text{n}}=111N.$ The spring is made from heat$-$treated steel with a hardness of $390$ Bhn and the spring's surface is ground. The theoretical stress concentration for bending is $K_t=1\mathrm{.}5$ at the support. Using the Goodman criterion to evaluate failure, will the spring fail in fatigue if cycled for ${10}^7$ cycles. Also, what is the factor of safety?